The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X
0 X 0 0 0 X X X 0 0 0 X 0 X X X 0 0 0 X X
0 0 X 0 X X X 0 0 0 X X X X 0 0 0 0 X X 0
0 0 0 X X 0 X X 0 X X 0 0 X X 0 0 X X 0 0
generates a code of length 21 over Z2[X]/(X^2) who´s minimum homogenous weight is 20.
Homogenous weight enumerator: w(x)=1x^0+18x^20+8x^22+4x^24+1x^40
The gray image is a linear code over GF(2) with n=42, k=5 and d=20.
As d=20 is an upper bound for linear (42,5,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in 0.00127 seconds.